21M.065—Introduction to Musical Composition
The following options can help you to achieve greater rhythmic contrast between
sections of a piece (e.g., opening and closing sections in a symmetric meter, contrasting
middle section based on additive rhythms).
(Items in boldface represent terms to know for the next quiz and/or final exam.)
mixed meters
use of two or more metric patterns (e.g., 6/8 alternating with 3/4)
Audio example: Bartók, “Syncopation” (from Mikrokosmos, Book V). Note the frequent changes
between 5/4 and 4/4 meters. Note furthermore that many of these bars, although beamed as five or four
quarters respectively, contain accents (the syncopations of the title) that effectively project additive
schemes of pulse organization (see below).
asymmetric meter
regularly recurring pattern based on beats of unequal length (e.g., 7/8 as 3+2+2)
For the sake of accuracy in performance, it’s more useful to think of these in terms of addition
(unequal groupings a regular fast pulse), rather than division (unequal beats).
ALTERNATIVES to METER
Unmeasured sustained/rolled tones (drones) effectively suspend any sense of
meter. In a similar vein, a flurry of extremely rapid notes without clear recurring accents
(of the sort that you heard in Ligeti’s Continuum for harpsichord) likewise can obliterate
any sense of regular pulse.
Audio examples: Ingram Marshall, Fog tropes; Conlon Nancarrow, Study no. 21 (Canon X).
additive rhythms
irregular rhythms that result from free groupings of a constant underlying pulse
Audio examples: Olivier Messiaen, “Danse de la fureur, pour les sept trompettes” [“Dance of fury,
for the seven trumpets”], from Quatuor pour la fin du temps [Quartet for the end of time]. This is an
example of freely additive rhythmic organization; listen for recurring motives of rhythm and pitch.
Philip Glass, “Spaceship,” from Einstein on the beach, Act IV, Scene 3. This is an example of
additive rhythms that the composer generally transforms according to incremental processes, though there
are more dramatic changes from time to time.
ASSIGNMENT for Tue, 18 Oct
Compose a piece for solo percussion, which you will perform for the class, based
on additive rhythms and/or mixed meters generated from a set of spoken phrases. Please
bring TWO copies (one for yourself, and one for me). Try to notate the rhythms as
completely as you can, using conventional notation with liberal use of accents. Be sure to
write the notes with beams that clarify the organization of pulses into (unequal) beats.
Using speech rhythms to generate additive rhythms and mixed meters
1. Start by choosing some words or phrases that vary in rhythm:
“thermophotovoltaic cell”
“light-emitting and absorbing material”
“silicon crystal”
2. Notate them as rhythmic motives
(NB the meter derives from the
smaller groups, and not vice versa)
















ther - mo - pho - to - vol - ta - ic
 
 

light - e - mit - ting


 
and


ab - sorb - ing





 

cell

ma - te - ri - als


si - li - con



crys - tal
3. Here's the beginning of a solo piece based on free combination, elision, extension,
multiplicative mapping, etc. of the above motives
Moderately fast

 ther - mo - pho - to - vol - ta - ic,
ther - mo - pho - to - vol - ta - ic,

si - li - con crys - tal,



                   


p



 ther - mo - pho - to - vol - ta - ic,

si - li - con crys - tal,
    

f
ther - mo - pho - to - vol - ta - ic, ther - mo - pho - to - vol - ta - ic,



                    



p


light e - mit - ting,
   
f
 ther - mo, ther - mo, ther - mo, ther - mo, 
 light e - mit - ting, light e - mit - ting, 
 light e - mit - ting and ab - sorb - ing ma - te - ri - als,
        
p
       
f
         
  
ff
f